高度非线性弹塑性模型的半隐式算法实现

Semi-implicit numerical integration of a highly nonlinear elasto-plastic constitutive model

对高度非线性弹塑性本构模型当采用全显式算法进行数值实现的过程中存在误差积累和精度较低的缺点。当采用Newton-CPPM隐式算法进行数值实现的过程中容易出现Jacobian矩阵奇异和不收敛问题。为提高精度、改善收敛性并提高计算效率,提出一种半隐式算法,并采用半隐式算法对Newton-CPPM算法的迭代初值进行改进,形成了改进的隐式算法。最后,以考虑结构性的SANICLAY模型为例,对全显式算法、半隐式算法、隐式算法和改进隐式算法在计算收敛性、计算效率和计算精度方面进行对比。结果表明,半隐式算法可以有效解决显式算法精度低和误差积累的缺点,其计算精度与改进后的隐式算法的计算精度相近。改进后的隐式算法可以有效解决Jacobian矩阵奇异和不收敛问题。

When implementing a highly nonlinear stress-strain model to solve boundary-valued problems,one of the major challenges is how to reduce the accumulative error and to maintain the effectiveness of the numerical integration. In general,the explicit algorithm tends to have higher accumulative error,and the requirement for accuracy may not be satisfied even when adopting very small increment sizes. When utilizing the Newton-CPPM implicit numerical integration algorithm,the complex Jacobian matrix for a highly nonlinear model may result in non-convergence or even become singular in the modelling process. In order to deal with these challenges,this paper proposes an improved-implicit algorithm,in which a semi-implicit method is used to determine the initial values for the implicit iterations. Using the highly nonlinear SANICLAY model for structured clay as an example,the convergence,the computational efficiency and the accuracy of four algorithms,namely the explicit algorithm,the semi-implicit algorithm,the implicit algorithm and the improved implicit algorithm,are compared via numerical simulations of single element tests. Comparing with the explicit algorithm,the semi-implicit algorithm effectively reduces error accumulation and improves the computation accuracy. The improved implicit algorithm can effectively improve convergence and avoid singularity of Jacobian matrix.